In this paper, a joint optimal design is investigated for orthogonal frequency division multiplexing (OFDM) systems to reduce peak interference-to-carrier ratio (PICR), out-of-band power (OBP) emissions, and peak-to-average power ratio (PAPR). Two approaches, namely, the phase rotation approach and the constellation extension approach, are proposed to convert this joint design problem into a second order cone programming (SOCP) problem, whose global optimal solution has been shown to exist and can be obtained efficiently. Simulation results are presented to demonstrate efficacy of the proposed algorithms in joint PICR, OBP, and PAPR reduction.